I am always impressed by a stadium full of people shouting or singing. Some are local and some are universal. Here are some local fan chants I know:

to the tune of "Go West" - "Steht auf, wenn Ihr Mainzer seid. steht auf, wenn Ihr Mainzer seid..." (stand up if you are from Mainz...)I think this is universal

to the tune of Yellow Submarine:

"Wir sind nur ein Karnevalsverein, Karnevalsverein, Karnevalsverein... " meaning: "we are just a carnival club, carnival club etc" - a tune brought up by the local rivals from Frankfurt who sang : YOU are just...". The fans from Mainz took up the tune in self mockery and now they have a couple of other local carnival songs in their catalogue (Mainz has a carnival tradition), for example "Humba humba täterrää" which is self explaining and has been adopted by other fans from the premier league :)

"Du hast die Haare schön, Du hast die Haare schön" is a cool chant from Mainz, I don't know where the tune comes from, it's used for other football chants, too. It means "you have your hair done nicely" and it started when a striker, who happend to have a new hairdo that day, missed the goal from 2 meters. Now it's always used to make fun of a player who makes a very stupid mistake.

Vieira, whoa-oh, he gave Giggsy the ball, and Arsenal won fuck all (Volare)

One the twelfth day of Christmas, my true love gave to me... Twelve Cantonas, Eleven Cantonas, Ten Cantonas, Nine Cantonas, Eight Cantonas, Seven Cantonas, Six Cantonas, FIVE CANTONAS....Four Cantonas, Three Cantonas, Two Cantonas, and an Eric Cantona.

Oh Stevie Bull's a ta ta, He wears and England Cap, He plays for Wolverhampton, He is a lovely chap. He scores with his left foot, He scores with his right, And when we play the Albion, He'll score all fuckin' night.

Fight fight, wherever you may be, We are the boys from the Black country, We'll fight you all wherever you may be, Cos we are the boys from the Black country, (We dont river dance to that one though!)

I was born under a Wanderers scarf... Do you know where hell is, hell is at West Brom, Heaven is the Molineux and that is where we're from... I was born under a Wanderers scarf.

Its originally started as an inside joke on the Cross Country team (long distance running)... There was a wooden duck they would take everywhere so they would chant "QUACK,QUACK..." etc etc... And being teens with raging hormones, they love to make things dirty, and BJ stands for uhh.... god this is nasty... Blow Job....

And then it spread and eventually pretty much everyone in school was chanting it...

Its originally started as an inside joke on the Cross Country team (long distance running)... There was a wooden duck they would take everywhere so they would chant "QUACK,QUACK..." etc etc... And being teens with raging hormones, they love to make things dirty, and BJ stands for uhh.... god this is nasty... Blow Job....

And then it spread and eventually pretty much everyone in school was chanting it...